You jump off the end of a ski jump. Your height in meters relative to the height of the ski jump after t seconds is given by h(t)=-5t^(2)+12t. How high will you be compared to the end of the ski jump after 6 seconds?
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- The acceleration of a particle is a constant. At t=0 the velocity of the particle is (14.91 + 18.4ĵ) m/s. At t = 4.6 s the velocity is 11.4j m/s. (Use the following as necessary: t. Do not include units in your answers.) (a) What is the particle's acceleration (in m/s²)? = î+ 18.4 v(t) = (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin. r(t) = î+ X Î- i) m/s m/sA rodeo horse is running around a corral at a speed of 300 ft/s. Let x(t) be the distance of the horse from the third barrel and y(t) his distance from the fourth. (see figure; note that the distance between barrels is 900 řt). At what rate is the horse's distance from the fourth barrel changing at the instant when he is 200 ft from the third? 2 1 3 4Suppose a migrating bird flies at a constant altitude of 5 km, with a velocity of 42 km/h. At time t = 0 the bird passes directly above a radar station, where t is measured in hours. (a) How fast is the distance between the bird and the radar station changing after 10 minutes? Round your final answer to 2 decimal places and provide units. (b) How fast is the distance between the bird and the radar station changing at time t = 0, i.e. when the bird is directly above the radar station? Is this reasonable? Explain briefly.
- A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 20 ft/s. 90 ft (a) At what rate is his distance from second base decreasing when he is halfway to first base? (Round your answer to one decimal place.) ft/s (b) At what rate is his distance from third base increasing at the same moment? (Round your answer to one decimal place.) ft/s Need Help? Read ItA skater with mass 66 kg is skating on a horizontal surface at a constant speed 4.2 m/s. There is a ramp ahead, and the skater has just enough speed to make it to the top of the ramp (meaning the speed at the top of the ramp is 0 m/s). What is the height of the ramp in the unit of meters? Use g = 10 m/s2 for the acceleration due to gravity.A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 46 ft/s. Its height in feet after t seconds is given by y = 46t – 21t2. A. Find the average velocity for the time period beginning when t=2 and lasting .01 s: .005 s: .002 s: .001 s: NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator. Estimate the instanteneous velocity when t=2.
- A rocket is fired upward with a velocity (v) of 590 feet per second. find how many seconds pass before the rocket reaches the ground (s=0) again. use the quadratic equation s=-16t^2+590t.How would I begin to solve this problem? In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)A space probe on the surface of Mars sends a radio signal back to the Earth, a distance of 7.96 ✕ 107 km. Radio waves travel at the speed of light (3.00 ✕ 108 m/s). How many seconds does it take for the signal to reach the Earth?